Subject: [mg90968] Re: [mg90956] Re: [mg90947] When is a List not a List?

From: DrMajorBob <drmajorbob at att.net>

Date: Fri, 1 Aug 2008 02:59:38 -0400 (EDT)

References: <200807310656.CAA07700@smc.vnet.net>

Reply-to: drmajorbob at longhorns.com

No argument here. That's the behavior, and we've seen it a thousand times.
A "quirk" is only a quirk the first 100 times we see it, or thereabouts.
(Pick a number.)
Plot COULD assign colors after evaluation, OTOH... the fact that it
doesn't is a design choice/artifact, not a necessity preordained by fate.
That being so, users are entitled to find it odd at first glance. (Or even
second... maybe third.)
Bobby
On Thu, 31 Jul 2008 13:56:56 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl>
wrote:
> When I wrote "Plot does not evaluate its arguments" I meant it in the
> usual (although inaccurate) sense that people frequently use in this
> context, namely: that the so called Evaluator does not pre-evaluate the
> arguments of Plot (if you do not like to thing of "the Evaluator",
> another way of saying this is that "Mathematica" does not evaluate the
> arguments before Plot is applied and leaves any evaluating to Plot.) Of
> course, you are right that Plot does evaluate its arguments in some way
> (this sort of behavior is also referred in the often used phrase: "Plot
> evaluates its arguments in a non-standard way"). The fact that this
> "non-standard" evaluation results in a plot of a function is actually
> new in version 6; in all previous versions all you will get is an error
> message about the values of the function being plotted not being numeric.
> Anyway, my point was that this has been a normal (non quirky) behavior
> of Mathematica since version 1 and has been discussed here a number of
> times. (It must be at least the fourth of fifth time in 10 years that I
> am addressing this issue on this forum). It is also fully documented
> (with examples) in the Mathematica online documentation, all past
> printed documentation and a vast number of books dealing with
> Mathematica.
>
> Andrzej Kozlowski
>
>
> On 31 Jul 2008, at 20:15, DrMajorBob wrote:
>
>> But Plot DOES evaluate its arguments, of course, and DOES (eventually)
>> see that multiple functions are being plotted. (Else they couldn't be
>> plotted.)
>>
>> It's just not happening before colors are assigned.
>>
>> Nonetheless, it's prudent to take note of what functions actually do,
>> and get used to it. Calling everything in sight a quirk serves no
>> purpose.
>>
>> (Paraphrasing Andrzej, perhaps.)
>>
>> Bobby
>>
>> On Thu, 31 Jul 2008 05:04:10 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl
>> > wrote:
>>
>>> There is nothing at all quirky about this. Yes, FullForm[Table[g[x,
>>> n], {n, 1, 2}]] and FullForm[{g[x, 1], g[x, 2]}] are indeed identical,
>>> but that is because FullForm evaluates its argument. But Plot has
>>> attribute:
>>>
>>> In[2]:= Attributes[Plot]
>>> Out[2]= {HoldAll, Protected}
>>>
>>> so, unlike FullForm, it does not evaluate its argument. In your first
>>> example, Plot[{g[x, 1], g[x, 2]}, {x, 0, 1}, PlotStyle -> {Red,
>>> Blue}], the first argument of Plot has an explicit List bracket, so
>>> Plot can see that it supposed to treat the argument as two different
>>> functions, without evaluating the argument. But in the second case, it
>>> does not see an explicit bracket, so it treats the entire expression
>>> as the graph of a single function (in versions of Mathematica before 6
>>> you would not have got any plot at all in this case).
>>>
>>> If you use Evaluate in the second code you will get the same result as
>>> you get form the first:
>>>
>>> Plot[Evaluate[Table[g[x, n], {n, 1, 2}]], {x, 0, 1}, PlotStyle ->
>>> {Red, Blue}]
>>>
>>> Finally, since you have given ample proof that, in spite of many years
>>> of using Mathematica, you have not mastered its basics (this
>>> particular issue has been raised and answered a countless number of
>>> times on this forum), why do you keep assuming that the problems that
>>> you keep coming across are Mathematica's "quirks" rather than (as is
>>> much more likely) gaps in your won understanding? What do you think of
>>> first year undergraduate students who whenever they do not understand
>>> something in their introductory lectures claim that it is wrong, or
>>> blame their textbook or their lecture rather then themselves?
>>>
>>> Andrzej Kozlowski
>>>
>>>
>>>
>>> On 31 Jul 2008, at 08:56, AES wrote:
>>>
>>>> g[x_, n_] := x^n
>>>> FullForm[Table[g[x, n], {n, 1, 2}]]
>>>> FullForm[{g[x, 1], g[x, 2]}]
>>>> Plot[{g[x, 1], g[x, 2]}, {x, 0, 1}, PlotStyle -> {Red, Blue}]
>>>> Plot[Table[g[x, n], {n, 1, 2}], {x, 0, 1}, PlotStyle -> {Red, Blue}]
>>>>
>>>> The FullForm[]s are identical. One Plot[] has red and blue curves;
>>>> the
>>>> other has two blue curves.
>>>>
>>>> Quirky!
>>>>
>>>
>>>
>>>
>>
>>
>>
>> --DrMajorBob at longhorns.com
>
>
--
DrMajorBob at longhorns.com